The data set for this project was obtained from Kaggle. This dataset is divided into two main classes of tumors malign or benign. Each tumor is described using several features computed from digital images taken from a fine needle aspirate of a breast lump. These describes the characteristics of a cell nucleus in a three dimensional space. The characteristics include radius, texture, perimeter, smoothness, compactness and concavity to name a few.
The data consist of 357 benign tumors and 212 malignant tumors. The data consist of 30 features in which all them are numeric with the exception of the diagnosis feature. The feature called “id” does not provide value for the model since it represents a unique identifier. As a result, this feature will be dropped from the model. The target feature diagnosis has two values M for malign and B for benign. Such feature will be extracted and the remaining 28 features will be used for training and testing the model.
Exploring the Data¶
# Import libraries
import numpy as np
import pandas as pd
from time import time
from sklearn.metrics import f1_score
# Read tumor data
tumorData = pd.read_csv("breast_cancer.csv")
print "Data read successfully!"
Data Exploration¶
Let's begin by investigating the dataset to determine how many tumors we have information on, and learn about the malign and benign rate among these lumps. In the code cell below, the following values are compute:
- The total number of tumors,
nTumor. - The total number of features for tumor,
nFeature. - The number of those tumors that are benign,
nBening. - The number of those tumors that are malign,
nMalign.
from IPython.display import display
# Calculate number of tumors
nTumor = tumorData.shape[0]
# Calculate number of features
nFeature = len(tumorData.columns)
# Calculate the number of benign tumors
nBenign = tumorData[tumorData['diagnosis'] == 'B'].shape[0]
# Calculate the number of malign tumors
nMalign = len(tumorData[tumorData['diagnosis'] == 'M'])
# Calculate malign lump rate
malignRate = float (nMalign) / nTumor * 100
# Print the results
print "Total number of Tumors: {}".format(nTumor)
print "Number of features: {}".format(nFeature)
print "Number of Benign Tumors: {}".format(nBenign)
print "Number of Malign Tumors: {}".format(nMalign)
print "Malign rate : {:.2f}%".format(malignRate)
Identify feature and target columns¶
It is often the case that the data you obtain contains non-numeric features. This can be a problem, as most machine learning algorithms expect numeric data to perform computations with. In the cell below the dataset is explore in detail to determine if non-numeric values needs to be transformed to numeric values.
# Extract feature columns
feature = list(tumorData.columns[2:-1])
# Extract target column 'passed'
target = tumorData.columns[1]
# Show the list of columns
print "Feature #{} columns:\n{}".format(len(feature), feature)
print "\nTarget column: {}".format(target)
# Separate the data into feature data and target data (X_all and y_all, respectively)
X_all = tumorData[feature]
y_all = tumorData[target]
# Show the feature information by printing the first five rows
print "\nFeature values:"
tumorData[tumorData.columns[:9]].head()
Training and Testing Data Split¶
For the next step, we split the data (both features and corresponding labels) into training and test sets. In the following code cell below the following steps will be performed:
- Randomly shuffle and split the data (
X_all,y_all) into training and testing subsets.- Use 455 training points (approximately 80%) and 114 testing points (approximately 20%).
- Set a
random_statefor the function(s) you use, if provided. - Store the results in
X_train,X_test,y_train, andy_test.
# Import any additional functionality you may need here
from sklearn.model_selection import train_test_split
from sklearn.model_selection import KFold
# Define KFold cross-validation that will be used later on
k_fold = KFold(n_splits=5, random_state=20, shuffle=True)
# Set the number of training points
num_train = 455
# Set the number of testing points
num_test = X_all.shape[0] - num_train
test_size = num_test * 1.0 / X_all.shape[0]
# Shuffle and split the dataset into the number of training and testing points above
X_train, X_test, y_train, y_test = train_test_split(X_all, y_all, test_size=test_size, random_state=20)
# Show the results of the split
print "Training set has {} samples.".format(X_train.shape[0])
print "Testing set has {} samples.".format(X_test.shape[0])
Data Preprocessing¶
Determine if the dataset is normally distributed using scatter plot matrix.
import matplotlib.pyplot as plt
color_function = {"B": "blue", "M": "red"} # Here Red color will be 1 which means M and blue foo 0 means B
colors = tumorData["diagnosis"].map(lambda x: color_function.get(x))# mapping the color fuction with diagnosis column
# plotting scatter plot matrix
pd.scatter_matrix(tumorData[tumorData.columns[1:11]], c=colors, alpha = 0.5, figsize = (15, 15), diagonal = 'kde')
plt.show()
pd.scatter_matrix(tumorData[tumorData.columns[11:21]], c=colors, alpha = 0.5, figsize = (15, 15), diagonal = 'kde')
plt.show()
pd.scatter_matrix(tumorData[tumorData.columns[21:31]], c=colors, alpha = 0.5, figsize = (15, 15), diagonal = 'kde')
plt.show()
Feature Scaling¶
If data is not normally distributed, especially if the mean and median vary significantly (indicating a large skew), it is most often appropriate to apply a non-linear scaling — particularly for financial data. One way to achieve this scaling is by using a Box-Cox test, which calculates the best power transformation of the data that reduces skewness. A simpler approach which can work in most cases would be applying the natural logarithm. In the code block below, the following will be performed:
- Assign a copy of the data to logData after applying logarithmic scaling. Use the np.log function for this.
- Assign a copy of the sample data to logData after applying logarithmic scaling. Again, use np.log.
import numpy as np
# Scale the data using the natural logarithm
logData = np.log(X_all)
#print np.where(np.isnan(logData))
#print np.where(np.isinf(logData))
#print np.isnan(logData.values.any())
logData = logData.replace([np.inf, -np.inf], 0.0)
logData.fillna(0.0, inplace=True)
X_all = logData.copy(deep=True)
logData = pd.concat([logData, y_all], axis=1)
# mapping the color fuction with diagnosis column
colors = logData["diagnosis"].map(lambda x: color_function.get(x))
# plotting scatter plot matrix
pd.scatter_matrix(logData[logData.columns[1:11]], c=colors, alpha = 0.5, figsize = (15, 15), diagonal = 'kde')
plt.show()
# plotting scatter plot matrix
pd.scatter_matrix(logData[logData.columns[11:21]], c=colors, alpha = 0.5, figsize = (15, 15), diagonal = 'kde')
plt.show()
# plotting scatter plot matrix
pd.scatter_matrix(logData[logData.columns[21:31]], c=colors, alpha = 0.5, figsize = (15, 15), diagonal = 'kde')
plt.show()
Feature Transformation¶
In this section the use principal component analysis (PCA) to draw conclusions about the underlying structure of the data. Since using PCA on a dataset calculates the dimensions which best maximize variance, we will find which compound combinations of features best describe tumors.
PCA¶
Now that the data has been scaled to a more normal distribution, we can now apply PCA to the data to discover which dimensions about the data best maximize the variance of features involved. In addition to finding these dimensions, PCA will also report the explained variance ratio of each dimension — how much variance within the data is explained by that dimension alone. Note that a component (dimension) from PCA can be considered a new "feature" of the space, however it is a composition of the original features present in the data.
In the code block below, the following steps were performed:
- Define a plot function to visualize the result of PCA
- Import
sklearn.decomposition.PCAand assign the results of fitting PCA in ten dimensions withdatatopca.
def pca_plot(good_data, pca):
'''
Create a DataFrame of the PCA results
Includes dimension feature weights and explained variance
Visualizes the PCA results
'''
# Dimension indexing
dimensions = dimensions = ['Dimension {}'.format(i) for i in range(1,len(pca.components_)+1)]
# PCA components
components = pd.DataFrame(np.round(pca.components_, 4), columns = good_data.keys())
components.index = dimensions
# PCA explained variance
ratios = pca.explained_variance_ratio_.reshape(len(pca.components_), 1)
variance_ratios = pd.DataFrame(np.round(ratios, 4), columns = ['Variance'])
variance_ratios.index = dimensions
# Create a bar plot visualization
fig, ax = plt.subplots(figsize = (14,8))
# Plot the feature weights as a function of the components
components.plot(ax = ax, kind = 'bar');
ax.set_ylabel("Feature Weights")
ax.set_xticklabels(dimensions, rotation=0.5)
# Display the explained variance ratios
for i, ev in enumerate(pca.explained_variance_ratio_):
ax.text(i-0.40, ax.get_ylim()[1] + 0.05, "Variance\n %.4f"%(ev))
# Return a concatenated DataFrame
return pd.concat([variance_ratios, components], axis = 1)
from sklearn.decomposition import PCA
# Apply PCA by fitting the good data with the same number of dimensions as features
pca = PCA(n_components=10)
pca.fit(X_all)
# Generate PCA results plot
pca_result = pca_plot(X_all, pca)
plt.show()
Define the proper dimensionality of the data: PCA¶
Since beyond the dimension '#7 the model barely improves by 1% is not worth to go beyond this point.
# Apply PCA by fitting the good data with only two dimensions
pca = PCA(n_components=7)
pca.fit(X_all)
# Transform the good data using the PCA fit above
reduced_data = pca.transform(X_all)
# Create a DataFrame for the reduced data
reduced_data = pd.DataFrame(reduced_data, columns = ['Dimension 1', 'Dimension 2', 'Dimension 3', 'Dimension 4',
'Dimension 5', 'Dimension 6', 'Dimension 7'])
latestData = pd.concat([reduced_data, y_all], axis=1)
pd.scatter_matrix(latestData, c=colors, alpha = 0.5, figsize = (15, 15), diagonal = 'kde')
plt.show()
Data Split of the PCA dataset¶
The pca data (reduced_data) will be split into training and test sets. In the following code cell below, the following steps will be performed:
- Randomly shuffle and split the data (X_all, y_all) into training and testing subsets.
- Use 455 training points (approximately 80%) and 114 testing points (approximately 20%).
- Set a random_state for the function(s) you use, if provided.
- Store the results in X_train, X_test, y_train, and y_test.
# Shuffle and split the dataset into the number of training and testing points above
X_train, X_test, y_train, y_test = train_test_split(reduced_data, y_all, test_size=test_size, random_state=20)
# Show the results of the split
print "Training set has {} samples.".format(X_train.shape[0])
print "Testing set has {} samples.".format(X_test.shape[0])
Training and Evaluating Models¶
In this section, different supervised learning models that are appropriate will be used for this problem and available in scikit-learn. Then fit the model and measure the F1 score.
The following supervised learning models are currently available in scikit-learn and all of them will be evaluated:
- Gaussian Naive Bayes (GaussianNB)
- Decision Trees
- Random Forest
- K-Nearest Neighbors (KNeighbors)
- Support Vector Machines (SVM)
Setup¶
The code cell below to initialize three helper functions which you can use for training and testing the supervised learning models. The functions are as follows:
train_classifier- takes as input a classifier and training data and fits the classifier to the data.predict_labels- takes as input a fit classifier, features, and a target labeling and makes predictions using the F1 score.train_predict- takes as input a classifier, and the training and testing data, and performstrain_clasifierandpredict_labels.- This function will report the F1 score for both the training and testing data separately.
def train_classifier(clf, X_train, y_train):
''' Fits a classifier to the training data. '''
# Start the clock, train the classifier, then stop the clock
start = time()
clf.fit(X_train, y_train)
end = time()
# Print the results
print "Trained model in {:.4f} seconds".format(end - start)
def predict_labels(clf, features, target):
''' Makes predictions using a fit classifier based on F1 score. '''
# Start the clock, make predictions, then stop the clock
start = time()
y_pred = clf.predict(features)
end = time()
# Print and return results
print "Made predictions in {:.4f} seconds.".format(end - start)
return f1_score(target.values, y_pred, pos_label='M')
def train_predict(clf, X_train, y_train, X_test, y_test):
''' Train and predict using a classifer based on F1 score. '''
# Indicate the classifier and the training set size
print "Training a {} using a training set size of {}. . .".format(clf.__class__.__name__, len(X_train))
# Train the classifier
train_classifier(clf, X_train, y_train)
# Print the results of prediction for both training and testing
print "F1 score for training set: {:.4f}.".format(predict_labels(clf, X_train, y_train))
print "F1 score for test set: {:.4f}.".format(predict_labels(clf, X_test, y_test))
print "\n"
Model Performance Metrics¶
With the predefined functions above, each supervised learning models will make use of the train_predict function. The cell below implements the following steps:
- Import the five supervised learning models you've discussed in the previous section.
- Initialize the five models and store them in
clf_A,clf_B,clf_C,clf_Dandclf_E.- Use a
random_statefor each model. - Note: The default settings for each model will be used.
- Use a
- Create the different training set sizes to be used to train each model.
- Fit each model with each training set size and make predictions on the test set.
# from sklearn import model_A
from sklearn.svm import SVC
# from sklearn import model_B
from sklearn.naive_bayes import GaussianNB
# from sklearn import model_C
from sklearn.tree import DecisionTreeClassifier
# from sklearn import model_D
from sklearn.neighbors import KNeighborsClassifier
# from sklearn import model_E
from sklearn.ensemble import RandomForestClassifier
# Initialize the supervised models
randomState = 20
clf_A = SVC(random_state=randomState)
clf_B = GaussianNB()
clf_C = DecisionTreeClassifier(random_state=randomState)
clf_D = KNeighborsClassifier()
clf_E = RandomForestClassifier(random_state=randomState)
# Execute the 'train_predict' function for each classifier and each training set size
classifiers = {"SVC" : clf_A, "GaussianNB" : clf_B, "DecisionTreeClassifier" : clf_C, "KNeighborsClassifier" : clf_D,
"RandomForestClassifier" : clf_E}
for clf in classifiers.keys() :
train_predict(classifiers[clf], X_train, y_train, X_test, y_test)
print "------------------------------------------------------------------------"
Choosing the Best Model¶
In this section, two models will be choose from the five supervised learning models the best models to use on the tumor data. Then grid search will be performed to optimize the model over the entire training set (X_train and y_train) by tuning few parameters for each model to improve upon the untuned model's F1 score. The use of learning curve will be considere to determine the best models that will be further analyzed.
import numpy as np
import matplotlib.pyplot as plt
from sklearn.naive_bayes import GaussianNB
from sklearn.svm import SVC
from sklearn.datasets import load_digits
from sklearn.model_selection import learning_curve
from sklearn.model_selection import ShuffleSplit
from sklearn.metrics import f1_score
from sklearn.metrics import make_scorer
def plot_learning_curve(estimator, title, X, y, ylim=None, cv=None,
n_jobs=1, train_sizes=np.linspace(.1, 1.0, 5)):
plt.figure()
plt.title(title)
if ylim is not None:
plt.ylim(*ylim)
plt.xlabel("Training examples")
plt.ylabel("Score")
scoring = make_scorer(f1_score, pos_label='M')
train_sizes, train_scores, test_scores = learning_curve(
estimator, X, y, cv=cv, n_jobs=n_jobs, train_sizes=train_sizes, scoring=scoring)
train_scores_mean = np.mean(train_scores, axis=1)
train_scores_std = np.std(train_scores, axis=1)
test_scores_mean = np.mean(test_scores, axis=1)
test_scores_std = np.std(test_scores, axis=1)
plt.grid()
plt.fill_between(train_sizes, train_scores_mean - train_scores_std,
train_scores_mean + train_scores_std, alpha=0.1,
color="r")
plt.fill_between(train_sizes, test_scores_mean - test_scores_std,
test_scores_mean + test_scores_std, alpha=0.1, color="g")
plt.plot(train_sizes, train_scores_mean, 'o-', color="r",
label="Training score")
plt.plot(train_sizes, test_scores_mean, 'o-', color="g",
label="Cross-validation score")
plt.legend(loc="best")
return plt
# Cross validation iterations to get smoother mean test and train
for clf in classifiers.keys() :
plot_learning_curve(classifiers[clf], clf, X_train, y_train, cv = k_fold)
plt.show()
Model Tuning¶
Fine tune the chosen models. Use grid search (GridSearchCV) by selecting few parameters (using different values for each parameter). In the code cell below, the following actions will be performed:
- Import
sklearn.grid_search.GridSearchCVandsklearn.metrics.make_scorer. - Create a dictionary of parameters that will be fine tune for the chosen model.
- Example:
parameters = {'parameter' : [list of values]}.
- Example:
- Initialize the classifier you've chosen and store it in
clf. - Create the F1 scoring function using
make_scorerand store it inf1_scorer.- Set the
pos_labelparameter to the correct value!
- Set the
- Perform grid search on the classifier
clfusingf1_scoreras the scoring method, and store it ingrid_obj. - Fit the grid search object to the training data (
X_train,y_train), and store it ingrid_obj.
# Make an f1 scoring function using 'make_scorer'
f1_scorer = make_scorer(f1_score, pos_label='M')
# Utility function to report best scores
def report(results, n_top=3):
for i in range(1, n_top + 1):
candidates = np.flatnonzero(results['rank_test_score'] == i)
for candidate in candidates:
print("Model with rank: {0}".format(i))
print("Mean validation score: {0:.3f} (std: {1:.3f})".format(
results['mean_test_score'][candidate],
results['std_test_score'][candidate]))
print("Parameters: {0}".format(results['params'][candidate]))
print("")
import itertools
from sklearn.metrics import confusion_matrix
def plot_confusion_matrix(cm, classes,
normalize=False,
title='Confusion matrix',
cmap=plt.cm.Blues):
"""
This function prints and plots the confusion matrix.
Normalization can be applied by setting `normalize=True`.
"""
if normalize:
cm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]
print("Normalized confusion matrix")
else:
print('Confusion matrix, without normalization')
print(cm)
plt.imshow(cm, interpolation='nearest', cmap=cmap)
plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(classes))
plt.xticks(tick_marks, classes, rotation=45)
plt.yticks(tick_marks, classes)
fmt = '.2f' if normalize else 'd'
thresh = cm.max() / 2.
for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):
plt.text(j, i, format(cm[i, j], fmt),
horizontalalignment="center",
color="white" if cm[i, j] > thresh else "black")
plt.tight_layout()
plt.ylabel('True label')
plt.xlabel('Predicted label')
# Import 'GridSearchCV' and 'make_scorer'
from sklearn.model_selection import GridSearchCV
# Create the parameters list you wish to tune
parameters = [
{'C': [1, 10, 100, 1000], 'kernel': ['linear']},
{'C': [1, 10, 100, 1000], 'gamma': [0.01, 0.001, 0.0001, 0.00001], 'kernel': ['rbf']},
]
# Initialize the classifier
svc = SVC(random_state=7)
# Perform grid search on the classifier using the f1_scorer as the scoring method
grid_obj = GridSearchCV(estimator = svc, param_grid = parameters, scoring = f1_scorer, cv = k_fold)
# Fit the grid search object to the training data and find the optimal parameters
grid_obj.fit(X_train, y_train)
# Get the estimator
clf = grid_obj.best_estimator_
print grid_obj.best_params_
# Report the final F1 score for training and testing after parameter tuning
print "Tuned model has a training F1 score of {:.4f}.".format(predict_labels(clf, X_train, y_train))
print "Tuned model has a testing F1 score of {:.4f}.".format(predict_labels(clf, X_test, y_test))
print " "
report(grid_obj.cv_results_)
plot_learning_curve(clf_A, "SVC Original", X_train, y_train)
plot_learning_curve(svc, "SVC Tuned", X_train, y_train)
plt.show()
y_pred = clf.fit(X_train, y_train).predict(X_test)
class_names = list(y_all.unique())
mtrx = confusion_matrix(y_test, y_pred)
np.set_printoptions(precision = 4)
plt.figure()
plot_confusion_matrix(mtrx, classes=class_names, title='Confusion matrix, without normalization')
plt.figure()
plot_confusion_matrix(mtrx, classes=class_names, normalize = True, title='Normalized confusion matrix')
plt.show()
# Import 'GridSearchCV' and 'make_scorer'
from sklearn.model_selection import GridSearchCV
# Create the parameters list you wish to tune
param_grid = {"max_depth": [3, None],
"max_features": [1, 2, 3, 4, 5, 6, 7],
"min_samples_split": [2, 3, 7, 11],
"min_samples_leaf": [2, 3, 7, 11],
"bootstrap": [True, False],
"criterion": ["gini", "entropy"]}
# Initialize the classifier
rfc = RandomForestClassifier(random_state=7, n_estimators=20)
# Perform grid search on the classifier using the f1_scorer as the scoring method
grid_obj = GridSearchCV(estimator = rfc, param_grid = param_grid, scoring = f1_scorer, cv = k_fold)
# Fit the grid search object to the training data and find the optimal parameters
grid_obj.fit(X_train, y_train)
# Get the estimator
clf = grid_obj.best_estimator_
print grid_obj.best_params_
# Report the final F1 score for training and testing after parameter tuning
print "Tuned model has a training F1 score of {:.4f}.".format(predict_labels(clf, X_train, y_train))
print "Tuned model has a testing F1 score of {:.4f}.".format(predict_labels(clf, X_test, y_test))
print " "
report(grid_obj.cv_results_)
plot_learning_curve(clf_E, "RandomForestClassifier Original", X_train, y_train)
plot_learning_curve(rfc, "RandomForestClassifier Tuned", X_train, y_train)
plt.show()
y_pred = clf.fit(X_train, y_train).predict(X_test)
class_names = list(y_all.unique())
mtrx = confusion_matrix(y_test, y_pred)
np.set_printoptions(precision = 4)
plt.figure()
plot_confusion_matrix(mtrx, classes=class_names, title='Confusion matrix, without normalization')
plt.figure()
plot_confusion_matrix(mtrx, classes=class_names, normalize = True, title='Normalized confusion matrix')
plt.show()
Benchmark Comparison¶
Fine tune the chosen model will be compared to the Dummy Classifier.
from sklearn.dummy import DummyClassifier
dc = DummyClassifier()
train_predict(dc, X_train, y_train, X_test, y_test)
y_pred = dc.fit(X_train, y_train).predict(X_test)
class_names = list(y_all.unique())
mtrx = confusion_matrix(y_test, y_pred)
np.set_printoptions(precision = 4)
plt.figure()
plot_confusion_matrix(mtrx, classes=class_names, title='Confusion matrix, without normalization')
plt.figure()
plot_confusion_matrix(mtrx, classes=class_names, normalize = True, title='Normalized confusion matrix')
plt.show()
